Blake Courter

For those of us who work in engineering and geometric modeling, “offset” is an everyday operation. We use it in 2D and 3D to produce curves and surfaces at constant distance from other curves and surfaces. With experience, we learn that offset can be failure-prone, especially with precise B-rep solids and meshes. Implicit modeling, in particular, the signed distance field (SDF) representation of shapes, offers robust offsetting, but again, with experience, we learn that the results aren’t always what we expect.

Take these three examples of an offset rectangle, created using three different “line joining” approaches that date back to the early days of 2D graphics and are built into your browser:

1 April 2023 (Fiction)

As mentioned yesterday, hyperbolic space is more spatially dense than Euclidean space, and therefore offers opportunities for higher performance and fidelity in engineering applications. In this case study, we’ll examine how to prepare ordinary Euclidean CAD and mesh geometry for embedding in hyperbolic space and manufacture in QE3D’s quantum entanglement production system.

Triangles in hyperbolic space

The key unit in any structural design, including beam lattices, is a triangle. In Euclidean space, the sum of the angles of set of triangles around a vertex must total 360°. In hyperbolic space, we can increase that total angle to any number we want, even ∞!

1 April 2023 (Fiction)

As the cost of fabricating high-fidelity, quantum-collapsed geometry becomes increasingly prevalent, as an industry, we’re forced to confront the following challenge: where are we going to put all of our crap? At QE3D, we’re hard at work to collapse wave functions in our commitment to enable more engineering design space.

You may wonder: how does the superposition of quantum entanglement and machine learning scintillate more room for our everyday carry? Indeed, our technology achieves for consumer products, implantable electronics, wearable devices, and sub-dermal surveillance exactly the same advantages parachute pants achieved for break dancers. With the supremacy of the mesoscale fully realized via TPMS, spinodal decomposition, and mixed topology lattices, from what extra space might we draw additional engineering acumen?

At QE3D, we manifest our quantum technology through three regimes for AI-driven, dimensionality enhanced, spatial domains.

On the Geometric Processing Worldwide Discord server, a frequent participant was lamenting the challenge of absorbing all the great work going on in computational geometry. It caused me to consider my own challenges with learning math.

For a long time I wanted to know math. I thought that I could learn what was out there but by glossing over the text and seeing the ideas, maintaining some sort of mental index to the math I might someday need to use. I would assume that the author’s introductory instructions to do the exercises didn’t apply to me. I usually only made it a few chapters into such texts.

My daughter, “X”, who just turned five, has been enjoying adding and subtracting small whole numbers in her head. She is just starting to write, so we made a little table for her to practice. Here she is adding:

Hello and welcome. Sometime around 2020, my old Amazon instance with Wordpress finally bit the dust. Here we are, trying again, with modern technology. Eventually, we’ll get some of the old content rehosted here.

Mark Burhop requested definitions of hipster geometry terms.

Okay, let's build off of the implicit chamfer thread to demonstrate how you can quickly produce any edge treatment you can dream of using implicit geometry.

In @ntopology, we'll deliver the holy grail of edge treatments: the C∞ blend.

Previous:https://t.co/uKOXYihBD5

(1/n) pic.twitter.com/UG7sRIbifa

— Blake Courter (@bcourter) June 25, 2022